Local Volatility Model: Dupire PDE and Valuation/Pricing PDE Derivations and Comparisons

Поделиться
HTML-код
  • Опубликовано: 24 дек 2024
  • Introduces the Local Volatility Model, and derives the Dupire PDE using two alternative approaches. Also compares and contrast the Dupire PDE against the Valuation/pricing PDE (this is kinda Black Scholes PDE), and the Fokker Planck Equation

Комментарии • 46

  • @TheSvram
    @TheSvram 2 года назад +3

    Good to see Lorenzo Bergomi's argument explained clearly by this video - Looking forward to see more videos of this especially touch basing the other concepts of stoch vol models.

  • @xianhuazhang2430
    @xianhuazhang2430 3 года назад +3

    Hi, really enjoy your detailed explains. But I still have a question: at 22:04, why the expectation of the second term does not have "Q" as the first term? Looking forward to your reply and thank you very much!

    • @quantpie
      @quantpie  3 года назад

      thank you, good spot! that is a typo!

  • @millamulisha
    @millamulisha 2 года назад

    Wow, your discussion around 6:00 is totally the result of bias-variance trade-off.

  • @sakuranooka
    @sakuranooka Год назад

    @21:00 Why can you replace d/dT by the partial derivative?

  • @wangchong1825
    @wangchong1825 4 года назад +1

    the video is wonderful! Which one of the video discusses the jump process?

    • @quantpie
      @quantpie  4 года назад

      thanks! We have started introducing jump processes in the Levy process playlist, there are 3 videos which cover different aspects of the Poisson, more videos to follow!

  • @hihihi82
    @hihihi82 3 года назад +4

    Hi, great series of video on financial mathematics! Seems very close to practical use instead of repeating what's in classical textbooks. May I ask whether you summarized these contents from original references paper? Could you please give some reference for the video?

    • @quantpie
      @quantpie  3 года назад +2

      Glad it was helpful! The material is quite standard; however, it is not based on particular book/article. If you take references in the Dupire's original paper, and complement them by those in Gatheral's then that should provide sufficient coverage of the topics covered in this video. many thanks!

  • @sakuranooka
    @sakuranooka Год назад

    In the local volatility SDE we have the term sigma(t, S), while all the PDE have sigma(T, K). How do these two relate to each other?

  • @khorweisheng9565
    @khorweisheng9565 3 года назад

    Hi, can u please explain at 25:09 the expectation return nonzero when K=S? a bit confuse here, thanks

  • @JitendraSingh-gn3oj
    @JitendraSingh-gn3oj 4 года назад +3

    HI Guys, Thank you so much for making the life easy. to apply the itos lema to absolute function can you plase name the formula. i couldnt catch it correctly

    • @quantpie
      @quantpie  4 года назад

      Thanks! It is called Tanaka Meyer, pls see here- en.m.wikipedia.org/wiki/Tanaka%27s_formula

  • @royleung4561
    @royleung4561 3 года назад +1

    HI , thank you for your vid. It is great. I have a question: what is the different between Dupirce 's local vol. model and those model like deterministic form for the vol, for example: CEV model ? Both of them are so- called local vol. model, but I can't relate them to each other. Thank you .

    • @quantpie
      @quantpie  3 года назад +1

      many thanks for the question! One is parametric (kinda assumes a particular functional form with some parameter whose value can be varied to get as close a fit as possible), and the second is non-parametric - it does not have a specific functional form, so shape is driven by the data. Hope this answers your question. Many thanks!

  • @franckherve981
    @franckherve981 5 лет назад +4

    Hi Guys, thank you for your videos..I think it will be also useful to make a videos on the avantages/drawbacks of these models on exotics products like barriere options, Autocall products etc...

  • @junwang0525
    @junwang0525 4 года назад +1

    Thank you!! How can we tell the Dupire is a forward PDE?

    • @quantpie
      @quantpie  4 года назад +1

      Thanks @Jun Wang! At least two ways to identify forward vs backward PDE in these settings: 1) via the sign of the second derivatives vs time derivative (please compare it to the Black Scholes PDE which is a backward PDE), and 2) via knowledge of the problem: initial vs terminal conditions and what dynamics is the PDE describing - here we have the initial condition S_0-K, and the PDE is in terms of the T (maturity), so it is a forward PDE. Hope it is clearer, but let me know if you have any further questions!

    • @junwang0525
      @junwang0525 4 года назад +1

      quantpie Thank you so much!

  • @greatjoeblack2202
    @greatjoeblack2202 Год назад

    Astonishing explanation!
    Masterpiece

  • @jacquesbagraim2516
    @jacquesbagraim2516 3 года назад +1

    Thank you for this informative and well-explained video - your video has helped me greatly so far with my dissertation. Much appreciated.

    • @quantpie
      @quantpie  3 года назад

      You’re welcome! Glad you found it useful! Thanks!

  • @biharlearning9294
    @biharlearning9294 Год назад

    Can you please share 2nd and 3rd order greeks for learning

  • @owenlai7101
    @owenlai7101 4 года назад +1

    Super wonderful! It's sooo clear and the video is awesome also!

    • @quantpie
      @quantpie  4 года назад

      Thank you! Cheers!

  • @dr.merlot1532
    @dr.merlot1532 3 года назад

    Are you using a textbook? Which one?

  • @ghostwhowalks5623
    @ghostwhowalks5623 3 года назад

    awesome video, and very nice to hear a human voice!!

    • @quantpie
      @quantpie  3 года назад

      Glad you liked it! thank you!

  • @anuragjain4474
    @anuragjain4474 4 года назад +1

    Beautifully explained. Also, can you provide the pdf so it will be easy for us to take notes.

    • @quantpie
      @quantpie  4 года назад

      As soon as possible! We have received this request many times, but unfortunately formatting the equations in a readable format requires work, and will switch to formatting as soon as we have finished the backlog!

  • @shyamrajgarhia8123
    @shyamrajgarhia8123 4 года назад +1

    Very clear in the explanation. Thank you

    • @quantpie
      @quantpie  4 года назад

      Glad it was helpful! You are welcome!

  • @franckherve981
    @franckherve981 5 лет назад +1

    Congratulations Guys.. keep going

    • @quantpie
      @quantpie  5 лет назад

      Thank you @Herve Franck!

  • @davide467
    @davide467 5 лет назад +2

    Great job as always

  • @wojciechkulma7748
    @wojciechkulma7748 2 года назад

    fantastic walkthrough, many thanks!

  • @JaGWiREE
    @JaGWiREE 5 лет назад +1

    Amazing as always!! Glad to see vids again :-)

  • @millypriest
    @millypriest 3 месяца назад

    really appreciate your video,that's will better if there is a script of this video for someone who is not good at listening english

  • @jasonsong4413
    @jasonsong4413 4 года назад

    This is so clear! Very much appreciated! :)

  • @Zorothustra
    @Zorothustra 5 лет назад +2

    Thanks for sharing!

    • @quantpie
      @quantpie  5 лет назад

      @M.Y., thank you!!

  • @智晖张
    @智晖张 Год назад

    hello, could I have your slides please? I am student and I am studying your lecture! its awesome!

  • @Accanfo
    @Accanfo 3 месяца назад

    Perfect